Absence of Solutions for Some Nonhomogeneous Elliptic Inequalities

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Abstract


By means of the modified method of test functions, we obtain sufficient conditions of absence of nontrivial solutions for some classes of semilinear elliptic inequalities of higher order and quasilinear elliptic inequalities containing nonhomogeneous terms (independent of the unknown function).


About the authors

E. I. Galakhov

Peoples’ Friendship University of Russia (RUDN University)

Author for correspondence.
Email: galakhov@rambler.ru
Moscow, Russia

O. A. Salieva

Peoples’ Friendship University of Russia (RUDN University)

Email: olga.a.salieva@gmail.com
Moscow, Russia

References

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  2. Похожаев С.И. Существенно нелинейные емкости, порожденные дифференциальными операторами// Докл. РАН. - 1997. -357. - С. 592-594.
  3. Galaktionov V., Mitidieri E., Pohozaev S. Blow-up for higher-order parabolic, hyperbolic, dispersion and Schrodinger equations. - Boca Raton: Chapman and Hall/CRC, 2014.¨
  4. Galakhov E., Salieva O. On blow-up of solutions to differential inequalities with singularities on unbounded sets// J. Math. Anal. Appl. - 2013. -408. - С. 102-113.
  5. Salieva O. On nonexistence of solutions to some nonlinear parabolic inequalities// Commun. Pure Appl. Anal. - 2017. -16, № 3. - С. 843-853.

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